Results 11 to 20 of about 350,847 (217)
CoRR, 2018 We introduce Reed-Solomon-Gabidulin codes which is, at the same time, an extension to Reed-Solomon codes on the one hand and Gabidulin codes on the other hand. We prove that our codes have good properties with respect to the minimal distance and design an efficient decoding algorithm.
Caruso, Xavier, Durand, Amaury
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MAKARA of Science Series, 2010 Reed Solomon (RS) codes is a mechanism to detect and correct burst of errors in data transmission and storage systems. It provides a solid introduction to foundation mathematical concept of Galois Field algebra and its application. With the development of digital hardware technology, the RS concepts were brought into reality, i.e. the implementation of
Petrus Mursanto
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The automorphisms and error orbits of Reed – Solomon codes
Доклады Белорусского государственного университета информатики и радиоэлектроники, 2020 The purpose of this work with its results presented in the article was to develop and transfer to the class of Reed – Solomon codes (RS-codes) the basic provisions of the theory of syndrome norms (TNS), previously developed for the noise-resistant coding
S. I. Semyonov, V. A. Lipnitsky
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Twisted reed-solomon codes [PDF]
2017 IEEE International Symposium on Information Theory (ISIT), 2017 In this article, we present a new construction of evaluation codes in the Hamming metric, which we call twisted Reed-Solomon codes. Whereas Reed-Solomon (RS) codes are MDS codes, this need not be the case for twisted RS codes. Nonetheless, we show that our construction yields several families of MDS codes. Further, for a large subclass of (MDS) twisted
Peter Beelen +2 more
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Repairing Reed-solomon codes [PDF]
Proceedings of the forty-eighth annual ACM symposium on Theory of Computing, 2016 We study the performance of Reed-Solomon (RS) codes for the \em exact repair problem \em in distributed storage. Our main result is that, in some parameter regimes, Reed-Solomon codes are optimal regenerating codes, among MDS codes with linear repair schemes.
Venkatesan Guruswami, Mary Wootters
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Balanced Reed-Solomon codes [PDF]
2016 IEEE International Symposium on Information Theory (ISIT), 2016 We consider the problem of constructing linear Maximum Distance Separable (MDS) error-correcting codes with generator matrices that are sparsest and balanced. In this context, sparsest means that every row has the least possible number of non-zero entries, and balanced means that every column contains the same number of non-zero entries.
Halbawi, Wael +2 more
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, 2021 Este trabalho apresenta a versão original dos Códigos de Reed-Solomon publicada em 1960 pelos matemáticos e engenheiros Irving Stoy Reed e Gustave Solomon.
Moura, Renata, Cornelissen, Mariana
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Quantum Reed—Solomon Codes [PDF]
, 1999 After a brief introduction to both quantum computation and quantum error correction, we show how to construct quantum error-correcting codes based on classical BCH codes. With these codes, decoding can exploit additional information about the position of errors. This error model - the quantum erasure channel - is discussed.
Markus Grassl +2 more
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Weighted Reed–Solomon convolutional codes
Linear and Multilinear Algebra, 2023 In this paper we present a concrete algebraic construction of a novel class of convolutional codes. These codes are built upon generalized Vandermonde matrices and therefore can be seen as a natural extension of Reed-Solomon block codes to the context of convolutional codes.
Alfarano, Gianira +3 more
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FNT-based reed-solomon erasure codes [PDF]
, 2009 This paper presents a new construction of Maximum-Distance Separable (MDS) Reed-Solomon erasure codes based on Fermat Number Transform (FNT). Thanks to FNT, these codes support practical coding and decoding algorithms with complexity O(n log n), where n ...
Soro, Alexandre +3 more
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